Early tetrapod cranial evolution is characterized by increased complexity, constraint, and an offset from fin-limb evolution.

The developmental underpinnings and functional consequences of modifications to the limbs during the origin of the tetrapod body plan are increasingly well characterized, but less is understood about the evolution of the tetrapod skull. Decrease in skull bone number has been hypothesized to promote morphological and functional diversification in vertebrate clades, but its impact during the initial rise of tetrapods is unknown. Here, we test this by quantifying topological changes to cranial anatomy in fossil and living taxa bracketing the fin-to-limb transition using anatomical network analysis. We find that bone loss across the origin of tetrapods is associated not only with increased complexity of bone-to-bone contacts but also with decreasing topological diversity throughout the late Paleozoic, which may be related to developmental and/or mechanical constraints. We also uncover a 10-Ma offset between fin-limb and cranial morphological evolution, suggesting that different evolutionary drivers affected these features during the origin of tetrapods.